Light irradiation apparatus, light irradiation method, crystallization apparatus, crystallization method, device, and light modulation element

ABSTRACT

A light irradiation apparatus includes a light modulation element which modulates a phase of an incident light beam to obtain a V-shaped light intensity distribution having a bottom portion of a minimum light intensity, and an image formation optical system which applies the modulated light beam from the light modulation element to an irradiation target surface in such a manner that the V-shaped light intensity distribution is provided on the irradiation target surface. The light modulation element has such a complex amplitude transmittance distribution that a secondary derivative of a phase value of a complex amplitude distribution becomes substantially zero at the bottom portion of the V-shaped light intensity distribution in an image space of the image formation optical system.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority fromprior Japanese Patent Application No. 2004-039747, filed Feb. 17, 2004,the entire contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a light irradiation apparatus, a lightirradiation method, a crystallization apparatus, a crystallizationmethod, a device, and a light modulation element.

2. Description of the Related Art

A thin film transistor (TFT) which is used for a switching element orthe like which selects a display pixel in, e.g., a liquid crystaldisplay (LCD) has been conventionally formed in an amorphous siliconlayer or a polysilicon layer.

The polysilicon layer has a higher mobility of electrons or holes thanthe amorphous silicon layer. Therefore, when a transistor is formed in apolysilicon layer, a switching speed is increased and a display responsespeed is thus increased as compared with a case where a transistor isformed in an amorphous silicon layer. Further, a peripheral LSI can bethereby formed of a thin film transistor. Furthermore, there is anadvantage that a design margin of any other component can be reduced.Moreover, peripheral circuits such as a driver circuit or a DAC can beoperated at a higher speed when these peripheral circuits areincorporated in a display.

Since polysilicon is formed of an aggregation of crystal grains, when,e.g., a TFT transistor is formed, a crystal grain boundary or boundariesexist in a channel area of such a transistor, and the crystal grainboundaries become an obstacle and lower the mobility of electrons orholes as compared with single-crystal silicon. Additionally, in case ofmany thin film transistors formed to polysilicon, the number of crystalgrain boundaries formed in channel portions differs between therespective thin film transistors, and this becomes unevenness intransistor characteristics and leads to a problem of displayirregularities in case of a liquid crystal display. Thus, in recentyears, in order to improve the mobility of electrons and holes andreduce irregularities in the number of crystal grain boundaries inchannel portions, there has been proposed a crystallization method whichgenerates crystallized silicon having crystal grains with a particlesize which is as large as one channel area can be formed in each crystalgrain.

As this type of crystallization method, there has been conventionallyknown a “phase control ELA (Excimer Laser Annealing) method” whichgenerates a crystallized semiconductor film by irradiating, with anexcimer laser light, a phase shifter which is closely arranged inparallel to a non-single-crystal semiconductor film such as apolysilicon semiconductor film or an amorphous semiconductor film. Thedetail of the phase control ELA method is described in, e.g., Journal ofthe Surface Science Society of Japan Vol. 21, No. 5, pp. 278-287, 2000.

In the phase control ELA method, a light intensity distribution havingan inverse peak pattern (a pattern in which a light intensity is minimumat the center (a minimum light intensity portion) and the lightintensity is suddenly increased toward the periphery or in the lateraldirection) in which the light intensity is lower than that at theperiphery is generated at a point or a line corresponding to a phaseshift portion of a phase shifter, and a non-single-crystal semiconductorfilm is irradiated with a light having this inverse-peak-shaped lightintensity distribution so that the non-single-crystal semiconductor filmis fused. As a result, a temperature gradient is generated in a fusingarea according to the light intensity distribution in an irradiationtarget area, a crystal nucleus is formed at a part which is solidifiedfirst or not solidified in accordance with the minimum intensityportion, and a crystal grows in a lateral direction from this crystalnucleus toward the periphery (which will be referred to as a “lateralgrowth” or a “growth in a lateral direction” hereinafter), therebygenerating a crystal grain with a large particle size.

Further, “Growth of Large Si Grains at Room Temperature byPhase-Modulated Excimer-Laser Annealing Method” by H. Ogawa et al.,IDW'03 Proceedings of The 10th International Display Workshops, p. 323brings forth a crystallization method which generates a crystal grain byirradiating a non-single-crystal semiconductor film with a light havinga V-shaped light intensity distribution obtained through a phase shifterand an image formation optical system. This reference discloses that itis desirable for an intensity distribution of a light which irradiatesthe non-single-crystal semiconductor film to vary in a V shape in arange of 0.5 to 1.0 when its maximum value is standardized as 1.0. The“light intensity distribution with the inverse peak pattern” and the“V-shaped light intensity distribution” have the same function as seenfrom each central portion (the minimum light intensity distribution andthe vicinity thereof). The both light intensity distribution are writtenas a “V-shaped light intensity distribution” in the present invention.

The inventors of the present application proposes a light modulationelement which can obtain a V-shaped light intensity distribution by acombination with an image formation optical system in, e.g., Jpn. Pat.Appln. No. 2003-117486 (which will be referred to as a “relatedapplication” hereinafter). The light modulation element proposed in therelated application is a “binary modulation type” phase shifter having areference phase value of 0 degree and a modulation phase value of 90degrees, i.e., two types of modulation phase values, which has a phasemodulation whose dimension is not greater than a point spread functionrange of an image formation optical system when converted into acounterpart on a light modulation element. Incidentally, it is needlessto say that disclosed matters in the related application do noconstitute a prior art of the present application.

Specifically, as shown in FIG. 14, a typical light modulation elementproposed in the related application has a reference phase area(indicated by a blank portion in the figure) 10 a having a referencephase value of 0 degree and rectangular phase-modulation areas(indicated by shaded portions in the figure) 10 b having a modulationphase value of 90 degrees. An occupied area ratio (a duty) of thephase-modulation areas 10 b to the reference phase area 10 a linearlyvaries between 0% and 50% along a horizontal direction (a lateraldirection) (along an X cross section) in the figure. Concretely, anoccupied area ratio of the phase-modulation areas 10 b is 0% on bothsides of a phase pattern along the horizontal direction, and an occupiedarea ratio of the phase-modulation areas is 50% at the center.

When such a light modulation element and an image formation opticalsystem which forms an image of a light modulated by this lightmodulation element on a non-single-crystal semiconductor film are used,such a V-shaped light intensity distribution as shown in FIGS. 15A to15C are obtained on the non-single-crystal semiconductor film. The lightintensity distributions shown in these figures are calculated on theassumption that a wavelength λ of an incident light beam is 248 nm, animage side numerical aperture NA of the image formation optical systemis 0.13 and a value σ (a coherence factor) of the image formationoptical system is 0.47. A light intensity I obtained at a focus positionor plane of the image formation optical system is dependent on anoccupied area ratio D (which varies between 0 and 0.5 in the exampleshown in FIG. 14) of the phase-modulation areas 10 b at a position inquestion along the X cross section, and approximately represented by thefollowing expression.I≈(4−4A)|D−0.5|²+A

-   -   where A≈cos²(θ/2)

In this expression, θ is a modulation phase value (90 degrees in theexample shown in FIG. 14), and A is a standardized value of a lightintensity obtained at a focus surface position corresponding to aposition where an occupied area ratio D is 50% on the maximum level (avalue when a maximum value of a light intensity in a V-shaped lightintensity distribution is standardized as 1.0).

When the light modulation element shown in FIG. 14 is used, asubstantially ideal V-shaped light intensity distribution which issubstantially symmetrical in a lateral direction with a minimumintensity portion at the center and whose formation position iscontrolled is formed at a focus position (an image formation surface) ofthe image formation optical system as shown in FIG. 15B. However, notonly a shape of the V-shaped light intensity distribution to be formedchanges but is asymmetrically varies depending on a defocusing directionat a position slightly moved from the focus position by 10 μm in adirection closer to the image formation optical system as shown in FIG.15A (a defocus position of −10 μm) or at a position slightly moved fromthe focus position by 10 μm in a direction apart from the imageformation optical system as shown in FIG. 15C (a defocus position of +10μm).

A board thickness deviation which can be a factor of defocusingunavoidably exists in a glass sheet used as a processed substrate havinga non-single-crystal semiconductor film formed thereon, which should beirradiated with a light. As a result, a shape of the V-shaped lightintensity distribution asymmetrically changes due to defocusing, and adesired V-shaped light intensity distribution cannot be stably formed ona non-single-crystal semiconductor film. Therefore, there occurs aninconvenience that crystal grains cannot be generated in substantiallyequal sizes in a semiconductor film on the processed substrate.Specifically, when slightly moved from the focus position by −10 μm asshown in FIG. 15A, a light intensity distribution in which two minimumlight intensity portions exist is formed, and hence a crystal growthstart point is divided into two points, thereby reducing a size of theproper crystal grain. Furthermore, as shown in FIG. 15C, in a lightintensity distribution formed at a position slightly moved from thefocus position by +10 μm, it can be understood that an uncrystallizedarea expands and a “filling factor of crystal grains” is reduced. Here,“the filling factor of crystal grains” is a ratio of a crystallized areato a light irradiation area when a non-single-crystal semiconductor filmis irradiated with a light beam having a V-shaped light intensitydistribution.

In a binary modulation type light modulation element, when a modulationphase value is set to 180 degrees rather than 90 degrees mentionedabove, a V-shaped light intensity distribution to be formed does notasymmetrically change in dependence on the defocusing direction.However, an attempt to assure the minimum light intensity portion to belarge to some extent in the V-shaped light intensity distribution with amodulation phase value being set to 180 degrees restricts a distributionof an occupied area ratio of phase-modulation areas having themodulation phase value to 0% to around 100%. This means that a phasearea having the modulation phase value or the reference phase valuebecomes extremely small, and also means that production of the binarymodulation type light modulation element whose modulation phase value is180 degrees is practically difficult.

BRIEF SUMMARY OF THE INVENTION

It is an object of the present invention to provide a crystallizationapparatus and a crystallization method which can stably form a desiredV-shaped light intensity distribution even if slightly moved from afocus position and can substantially evenly generate crystal grains on asemiconductor film.

According to a first aspect of the present invention, there is provideda light irradiation apparatus defined in claim 1.

It is preferable to satisfy the following conditions:(δ²δx²)arg(∫T(X,Y)dXdY)≈0(δ²/δy²)arg(∫T(X,Y)dXdY)≈0wherein (X,Y) is an in-plane coordinate of the light modulation element,T(X,Y) is a complex amplitude transmittance distribution of the lightmodulation element, (x,y) is an in-plane coordinate of an image surfaceof the image formation optical system, ∫ is an integration symbol in apoint spread function range of the image formation optical system wherea point on the light modulation element corresponding to the point (x,y)on the image surface is the center, and arg is a function which isrequired to obtain a phase value.

In the light irradiation apparatus, the complex amplitude transmittancedistribution of the light modulation element preferably has a phasemodulation unit whose size is not greater than a point spread functionrange of the image formation optical system. It is preferable that thelight modulation element has at least three types of phase areas havingfixed phase values different from each other and occupied area ratios ofthese areas vary in accordance with a predetermined pattern. In thiscase, it is preferable that the light modulation element comprises areference phase area having a reference phase value of 0 degree as areference, a first phase-modulation area having a first modulation phasevalue as a phase-modulation having a positive value, and a secondphase-modulation area having a second modulation phase value as a phasemodulation having a negative value which is substantially equal to anabsolute value of the first modulation phase value as at least threetypes of phase areas mentioned above. In this case, it is preferablethat a pattern with which an occupied area ratio of the firstphase-modulation area to the reference phase area varies issubstantially equal to a pattern with which an occupied area ratio ofthe second phase-modulation area to the reference phase area varies.

According to a second aspect of the present invention, there is provideda light irradiation method defined in claim 7.

According to a third aspect of the present invention, there is provideda crystallization apparatus comprising the light irradiation apparatusof the first aspect and a stage which holds a processed substrate havinga non-single-crystal semiconductor film on an image formation surface ofthe image formation optical system.

According to a fourth aspect of the present invention, there is provideda crystallization method which applies a light having the V-shaped lightintensity distribution to the processed substrate having anon-single-crystal semiconductor film set as the predetermined surfacein order to generate a crystallized semiconductor film by using thelight irradiation apparatus of the first aspect of the light irradiationmethod of the second aspect.

According to a fifth aspect of the present invention, there is provideda device manufactured by using the crystallization apparatus of thethird aspect or the crystallization method of the fourth aspect.

According to a sixth aspect of the present invention, there is provideda light modulation element defined in claim 11.

This light modulation element preferably comprises a reference phasearea having a reference phase value of 0 degree as a reference, a firstphase-modulation area having a first modulation phase value as aphase-modulation having a positive value, and a second phase-modulationarea having a second modulation phase value as a phase-modulation havinga negative value which is substantially equal to an absolute value ofthe first modulation phase value as at least three types of phase areasmentioned above. In this case, it is preferable that a pattern withwhich an occupied area ratio of the first phase-modulation area to thereference phase area varies is substantially equal to a pattern withwhich an occupied area ratio of the second phase-modulation area to thereference phase area varies.

Since the crystallization apparatus and the crystallization methodaccording to the present invention use a ternary modulation type lightmodulation element having such a complex amplitude transmittancedistribution that a secondary derivative of a phase value of the complexamplitude distribution becomes substantially zero at a bottom portion ofthe V-shaped light intensity distribution in an image space of the imageformation optical system, a desired V-shaped light intensitydistribution can be stably formed on a crystallization surface withoutbeing substantially affected by defocusing, and crystal grains withsubstantially equal sizes can be generated on the semiconductor film.

Additional objects and advantages of the invention will be set forth inthe description which follows, and in part will be obvious from thedescription, or may be learned by practice of the invention. The objectsand advantages of the invention may be realized and obtained by means ofthe instrumentalities and combinations particularly pointed outhereinafter.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate embodiments of the invention, andtogether with the general description given above and the detaileddescription of the embodiments given below, serve to explain theprinciples of the invention.

FIG. 1 is a view schematically showing a structure of a crystallizationapparatus according to an embodiment of the present invention;

FIG. 2 is a view schematically showing an internal structure of anillumination system depicted in FIG. 1;

FIGS. 3A to 3D are views respectively schematically showing an occupiedarea ratio, an absolute value of a complex amplitude distribution, aphase value of the complex amplitude distribution and a light intensitywhen generating a V-shaped light intensity distribution by using abinary modulation type light modulation element having a modulationphase value of 180 degrees;

FIGS. 4A to 4D are views respectively schematically showing an occupiedarea ratio, an absolute value of a complex amplitude distribution, aphase value of the complex amplitude distribution and a light intensitywhen generating a V-shaped light intensity distribution by using abinary modulation type light modulation element having a modulationphase value other than 180 degrees;

FIGS. 5A and 5B are views respectively schematically showing |U×Z| and aphase value of U×Z when generating a V-shaped light intensitydistribution by using a binary modulation type light modulation elementhaving a modulation phase value of 180 degrees;

FIGS. 6A and 6B are views respectively schematically showing |U×Z| and aphase value of U×Z when generating a V-shaped light intensitydistribution by using a binary modulation type light modulation elementhaving a modulation phase value other than 180 degrees;

FIG. 7 is a view illustrating that a secondary derivative of a phasevalue of a complex amplitude distribution U can be set to 0 in a ternarymodulation method;

FIGS. 8A and 8B are views of convolution associated with FIGS. 6A and6B, illustrating a principle of a defocus method;

FIG. 9 is a view schematically showing a phase pattern of a ternarymodulation type light modulation element according to the embodiment;

FIGS. 9A to 9G are process cross-sectional views showing an example of amanufacturing process for the ternary modulation type light modulationelement as shown in FIG. 9;

FIGS. 10A to 10C are views respectively showing a V-shaped lightintensity distribution formed through an image formation optical systemwhen the ternary modulation type light modulation element according tothe embodiment is used;

FIGS. 11A to 11C are first views schematically showing each V-shapedlight intensity distribution formed through an image formation opticalsystem when a binary modulation type light modulation element is used ina modification of the embodiment;

FIGS. 12A and 12B are second views schematically showing each V-shapedlight intensity distribution formed through an image formation opticalsystem when a binary modulation type light modulation element is used ina modification of the embodiment;

FIG. 12C is a view showing a corrected phase shifter according to amodification of the invention, and wave forms illustrating lightintensity distributions obtained by using the corrected phase shifter;

FIGS. 13A to 13E are process cross-sectional views showing processes ofmanufacturing an electronic device by using a crystallization apparatusaccording to the embodiment;

FIG. 14 is a view schematically showing a phase pattern of a binarymodulation type light modulation element proposed in a relatedapplication; and

FIGS. 15A to 15C are views schematically showing each V-shaped lightintensity distribution formed through an image formation optical systemwhen the light modulation element of FIG. 14 is used.

DETAILED DESCRIPTION OF THE INVENTION

An embodiment according to the present invention will now be describedwith reference to the accompanying drawings.

FIG. 1 is a view schematically showing a structure of a crystallizationapparatus according to an embodiment of the present invention. Moreover,FIG. 2 is a view schematically showing an internal structure of anillumination system. Referring to FIG. 1, the crystallization apparatusaccording to this embodiment includes a light modulation element 1 whichmodulates a phase of an incident light beam, an illumination system 2,an image formation optical system 3, and a substrate stage 5. Aprocessed substrate (a support substrate such as a glass substrate and anon-single-crystal semiconductor film directly or indirectly formedthereon) 4 is mounted on the stage 5. The detailed substructure and theeffects of the light modulation element 1 will be described later.

As shown in FIG. 2, the illumination system 2 includes a light source 2a which outputs an energy light which fuses the non-single-crystalsemiconductor film of the processed substrate 4. This light source is,e.g., a KrF excimer laser light source which supplies a pulse laser beamhaving a wavelength of, e.g., 248 nm. As this light source 2 a, it isalso possible to use any other appropriate light source such as an XeClexcimer laser light source or a YAG laser light source having aperformance which projects an energy light beam which fuses acrystallization target substance such as a non-single-crystalsemiconductor film. A laser beam exiting from the light source 2 a isexpanded through a beam expander 2 b and then enters a first fly-eyelens 2 c.

In this manner, a plurality of small light sources are formed on a rearfocal surface of the first fly-eye lens 2 c, and light rays from theplurality of small light sources illuminate an incident surface of asecond flu-eye lens 2 e in an overlapping manner through a firstcondenser optical system 2 d. As a result, more light sources than thoseon the rear focal surface of the first fly-eye lens 2 c are formed on arear focal surface of the second fly-eye lens 2 e. Light rays from theplurality of small light sources formed on the rear focal surface of thesecond fly-eye lens 2 e illuminate the light modulation element 1 in anoverlapping manner as a light beam, through the second condenser opticalsystem 2 f.

Here, the first fly-eye lens 2 c and the first condenser optical system2 d constitute a first homogenizer, and this first homogenizerhomogenizes an incidence angle of the laser beam supplied from the lightsource 2 a on the light modulation element 1. Additionally, the secondfly-eye lens 2 e and the second condenser optical system 2 f constitutea second homogenizer, and this second homogenizer homogenizes a lightintensity of the laser beam, whose incidence angle is homogenized by thefirst homogenizer, at any in-plane position on the light modulationelement 1. In this manner, the illumination system 2 illuminates thelight modulation element 1 with the laser beam having a substantiallyhomogeneous light intensity distribution.

The laser light or beam subjected to phase modulation by the lightmodulation 1 enters the processed substrate 4 through the imageformation optical system 3. Here, the image formation optical system 3arranges a pattern surface of the light modulation element 1 and theprocessed substrate 4 in an optically conjugate manner. In other words,a position of the processed substrate 4 is set on a surface (an imageplane of the image formation optical system 3) which is opticallyconjugate with the pattern surface or plane of the optical modulationelement 1. The image formation optical system 3 includes an aperturediaphragm 3 c between a positive lens assembly 3 a and a positive lensassembly 3 b.

The aperture diaphragm 3 c is one selected from a plurality of aperturediaphragms whose aperture positions (light transmission portions) havedifferent sizes. The plurality of aperture diaphragms 3 c are configuredto be replaceable with respect to an optical path. Alternatively, aniris diaphragm which can continuously change a size of the apertureportion may be used as the aperture diaphragm 3 c. In any case, a sizeof the aperture portion of the aperture diaphragm 3 c (which is thus animage side numerical aperture NA of the image formation optical system3) is set so that a necessary light intensity distribution is formed onthe semiconductor film of the processed substrate 4 as will be describedlater. The image formation optical system 3 may be a refraction typeoptical system, a reflection type optical system, or arefraction/reflection type optical system.

The non-single-crystal semiconductor film of the processed substrate 4is crystallized in processes of image formation of a laser beamphase-modulated by the light modulation element 1, fusion andsolidification. The processed substrate 4 is obtained by sequentiallyforming an underlying film and an amorphous silicon film (anon-single-crystal semiconductor film) on, e.g., a liquid crystaldisplay glass plate by chemical vapor deposition (CVD). The underlyinginsulating film is an insulating film of, e.g., SiO₂, avoids mixing offoreign particles such as Na into the amorphous silicon film from theglass substrate by direct contact of the amorphous silicon film and theglass substrate, and prevents a fusing temperature of the amorphoussilicon film from being directly transmitted to the glass substrate.

The non-single-crystal film is not restricted to the non-single-crystalsemiconductor film, and it may be, e.g., a metal other than asemiconductor. An insulating film such as an SiO₂ film as a cap film isformed on the amorphous silicon film. The cap film is heated by a partof the light beam which enters the amorphous silicon film, and stores aheated temperature. Although a temperature of a high-temperature portionis rapidly reduced on an irradiation target surface of the amorphoussilicon film when incidence of the light beam is interrupted, thisthermal storage effect alleviates this temperature drop gradient andfacilitates crystal growth with a large particle size in a lateraldirection. The processed substrate 4 is positioned and held at apredetermined position on the substrate stage 5 by a vacuum chuck, anelectrostatic chuck or the like.

Prior to explanation of a structure and effects of the light modulationelement 1 according to this embodiment, a description will now be givenas to a principle that a V-shaped light intensity distributionasymmetrically changes its shape in dependence on a defocusing direction(defocusing distance) when a binary modulation type light modulationelement having a modulation phase value other than 180 degrees is used.

In general, when the binary modulation type light modulation element isused, a complex amplitude distribution U at a focus position (a focalposition) where an optical image phase-modulated by the light modulationelement 1 is formed on the surface of the processed substrate 4 by theimage formation optical system 3 can be approximately represented by thefollowing Expression (1) while ignoring a proportionality coefficient(precisely, it is represented by convolution with a point spreadfunction). In Expression (1), (X,Y) is an in-plane coordinate of thelight modulation element, and T(X,Y) is a complex amplitudetransmittance distribution of the light modulation element. Further,(x,y) is an in-plane coordinate of an image surface (a focus position)of the image formation optical system, and ∫ is an integration symbol ina point spread function range of the image formation optical systemwhere a point on the light modulation element corresponding to the point(x,y) on the image surface is the center.U(x, y)≈∫T(X,Y)dXdY  (1)

That is, Expression (1) is led based on the following consideration.

The image formation by the image formation optical system is classifiedinto coherent image formation when illuminated by a point light source,incoherent image formation when illuminated by a perfect diffusion lightsource, and partial coherent image formation corresponding to anintermediate state of the both types of image formation. The imageformation by the actual optical system is the partial coherent imageformation, and its light intensity distribution can be obtained by anexpression led by H. H. Hopkins, but prospects are bad. Therefore, thediscussion will be given while approximating the coherent imageformation.

An amplitude distribution U(x,y) on the image surface in the coherentimage formation can be obtained by a convolution calculation representedby the following Expression (1-a). (M. Born and E. Wolf, Principle ofOptics, Chap. 9.5, 7th edition, Cambridge Univ. Press.)U(x,y)=∫∫T(X,Y)PSF(x−s,y−t)dXdY  (1-a)

-   -   wherein PSF(x,y) indicates an amplitude point spread function (a        complex amplitude distribution generated by a point object) of        the image formation optical system.

On the other hand, the amplitude point spread function is given byFourier transformation of a pupil function of the image formationoptical system. Assuming that a pupil has a circular shape and an eventransmittance, the amplitude point spread function PSF(x,y) can be givenby the following Expression (1-b). $\begin{matrix}{{{{PSF}\left( {x,y} \right)} = \frac{2{J_{1}\left( {2\pi\quad{{NAr}/\lambda}} \right)}}{2\pi\quad{{NAr}/\lambda}}}{r = \sqrt{x^{2} + y^{2}}}} & \left( {1\text{-}b} \right)\end{matrix}$wherein λ is a wavelength of a light beam, NA is a numerical aperture ofthe image formation optical system, and J₁ is a Bessel function.

Since it is hard to evaluate Expression (1-a) while keeping Expression(1-b), the amplitude point spread function is approximated with afunction of a cylindrical shape with a radius R which surrounds theamplitude point spread function, has a matching bottom surface and apeak value positioned on an upper surface thereof. That is, thefollowing expression can be obtained. $\begin{matrix}{{{PSF}\left( {x,y} \right)} = \left\{ {{\begin{matrix}1 & {r < R} \\0 & {r > R}\end{matrix}R} = {0.61{\lambda/{NA}}}} \right.} & \left( {1\text{-}c} \right)\end{matrix}$

-   -   wherein R is a minimum radius r with which a right side of        Expression (1-b) becomes 0. A range of a circular shape with the        radius R is referred to as the “point spread function range” and        represented by a symbol S. Then, Expression (1-a) is simplified        into an integration of a complex amplitude transmittance T(X,Yy)        in the point spread function range S with (x,y) at the center        like Expression (1).

The “point spread function range” means a range surrounded by a linewhich becomes 0 or can be regarded as 0 (substantially 0) in the pointspread function. In general, the point spread function range isrepresented by a circle which has a radius of 0.61λ/NA on the imagesurface assuming that NA is a numerical aperture of the image formationoptical system and λ is a wavelength of a laser beam used, and the pointspread function range has a value obtained by dividing this circle by amagnification on the light modulation element. Here, when the modulationphase value is 180 degrees, a value of the function T(X,Y) is a positivereal number in the reference phase area having a reference phase valueof 0 degree, and is a negative real number in the phase-modulation areahaving a modulation phase value of 180 degrees. In particular, even ifan occupied area ratio (a duty) of the phase-modulation area varies from0% to 5% as shown in FIG. 3A, a phase value of the complex amplitudedistribution U remains unchanged from 0 degree as shown in FIG. 3C. Itis to be noted that FIGS. 3A to 3D respectively schematically show anoccupied area ratio D, an absolute value of the complex amplitudedistribution U and a light intensity I (this value is in proportion to|U|²) when a V-shaped light intensity distribution is generated by usinga binary modulation type light modulation element having a modulationphase value of 180 degrees.

Alternatively, when a modulation phase value is a value θ other than 180degrees (θ≠180), a value of the function T(X,Y) is an imaginary number,and consequently a value of the complex amplitude distribution U is alsoan imaginary number. Further, when an occupied area ratio (a duty) ofthe phase-modulation area varies from 0% to 50% as shown in FIG. 4A, aphase value of the complex amplitude distribution U changes from 0degree to θ/2 as shown in FIG. 4C. FIGS. 4A to 4D respectivelyschematically show an occupied area ratio D, an absolute value |U| ofthe complex amplitude distribution U, a phase value of the complexamplitude distribution U and a light intensity I when a V-shaped lightintensity distribution is generated by using a binary modulation typelight modulation element having a modulation phase value other than 180degrees.

A description will now be given as to a change in light intensitydistribution caused due to defocusing when a binary modulation typelight modulation element is used. A complex amplitude distributionUd(x,y) at a defocus position is represented by the following Expression(2) (see “Optical Information Processing” by Junpei Tsujinai et al.,edited by The Japan Society of Applied Physics, Ohmsha, p. 8 and others,the entire contents of which are incorporated herein by reference).Ud(x,y)=U(x,y)*Z(x,y)  (2)

In Expression (2), * is an operator representing convolution(convolution integral), and U(x,y) is a complex amplitude distributionat a defocus position (a focal position) as described above.

In Expression (2), Z(x,y) is a point spread function expression Fresneldiffraction, and represented by the following Expression (3).Z(x,y)=exp{ik(x ² +y ²)/2 d}  (3)

-   -   where k=2π/λ

In Expression (3), k is a wave number, and d is a defocus quantity(defocus distance). As to a sign of d, a defocus quantity in a directionapart from the image formation optical system has a positive sign, and adefocus quantity in a direction closer to the image formation opticalsystem has a negative sign.

A condition of convolution at a point at the bottom of a V-shaped lightintensity distribution formed by using a binary modulation type likemodulation element will now be considered. FIG. 5A one-dimensionally (Xaxis) shows an absolute value |U×Z| of a value obtained by multiplyingU(x,y) by Z(x,y) in case of generating a V-shaped light intensitydistribution by using a binary modulation type light modulation elementhaving a modulation phase value of 180 degrees. However, in this case,an origin of Z is matched with the center of the V shape. That is,assuming that a central coordinate of the V shape is (x₀, y₀), there canbe achieved U×Z≡U(x,y)xZ(x−x₀,y−y₀). Furthermore, FIG. 6Aone-dimensionally (X axis) shows an absolute value |U×Z| of a valueobtained by multiplying U(x,y) by Z(x,y) in case of generating aV-shaped light intensity distribution by using a binary modulation typelight modulation element having a modulation phase value θ other than180 degrees (θ≠180). A result obtained by integrating |U×Z| shown inFIGS. 5A and 6A by the entire horizontal axis (a distance in the lateraldirection is indicated as a position of an A cross section) is thecomplex amplitude distribution at a point at the bottom of the V-shapedlight intensity distribution.

Since an absolute value |Z| of Z is 1, an absolute value |U×Z| of U×Z isequal to an absolute value |U| of U. Furthermore, by multiplying Z by U,a phase which is in proportion to a square of a distance from the pointin question is added. A sign of this phase increase corresponds to adefocus direction (a sign of a defocus quantity). That is, a sign of thephase increase is a positive sign in case of d>0, and a sign of thephase increase is a negative sign in case of d<0. As shown in FIG. 5B,in case of generating a V-shaped light intensity distribution by using abinary modulation type light modulation element having a modulationphase value of 180 degrees, a phase value of U×Z symmetrically varieswith respect to a sign of a defocus quantity d. Therefore, a result ofintegration involved by convolution also becomes symmetrical withrespect to a sign of the defocus quantity d.

Alternatively, as shown in FIG. 6B, in case of generating a V-shapedlight intensity distribution by using a binary modulation type lightmodulation element having a modulation phase value θ other than 180degrees (θ≠180), a phase value of U×Z asymmetrically varies with respectto a sign of a defocus quantity d. Therefore, a result of integrationinvolved by convolution also becomes asymmetrical with respect to a signof the defocus quantity d. In FIG. 5B, the defocus quantity drepresented in a phase term (a right side) of the equation (3) is adenominator, so that a parabola represented by the equation (3) becomesopen as the defocus quantity d increases.

Specifically, as apparent from FIG. 6B, in case of d>0, since a changequantity of a phase becomes small in the vicinity of a point inquestion, a light intensity is increased taking the integration intoconsideration. On the contrary, in case of d<0, since a change quantityof the phase becomes large in the vicinity of the point in question, alight intensity is reduced taking the integration into consideration.Such tendencies match with the calculation result mentioned above.

Summing up this consideration, it can be understood that a factor of theasymmetrical change of the V-shaped light intensity distribution withrespect to a sign of defocusing is that a phase value of U varies in asubstantially curved manner rather than a linear manner in accordancewith a bottom portion of |U×Z| at a focus position (d=0), namely, asecondary derivative of the phase value of U is not substantially zero.In other words, it can be understood that the V-shaped light intensitydistribution symmetrically varies with respect to a sign of defocusingby setting the secondary derivative of the phase value of U tosubstantially zero. As a solution for this problem, the presentinvention adopts the following two techniques.

The first technique is a “ternary modulation method” which sets asecondary derivative of a phase value of a complex amplitudedistribution as substantially zero at a bottom portion (the minimumlight intensity portion) of a V-shaped light intensity distribution inan image space of the image formation optical system by using a lightmodulation element having three or more types of modulation phasevalues, e.g., a ternary modulation type light modulation element havingone reference phase value and two modulation phase values. The secondtechnique is a “defocus method” which arranges an irradiation targetsurface at such a position that a secondary derivative of a phase valueof a complex amplitude distribution becomes substantially zero at abottom portion of a V-shaped light intensity distribution in an imagespace of the image formation optical system.

A description will be given as to an example where a secondaryderivative of a phase value of a complex amplitude distribution U can beset as zero in the ternary modulation method with reference to FIG. 7.In FIG. 7, a vertical axis I represents Imaginary, and a horizontal axisR represents Real. As an example, phases of three values are determinedas 0, +θ₀ and −θ₀. Integration in Expression (1) can be modified intothe following form. $\begin{matrix}{{U\left( {x,y} \right)} = {{U_{0}{\mathbb{e}}^{0i}} + {U_{1}{\mathbb{e}}^{+ {\theta 0i}}} + {U_{1}{\mathbb{e}}^{- {\theta 0i}}}}} \\{= {U_{0} + {U_{1}\left( {{\cos\quad\theta_{0}} + {{\mathbb{i}sin}\quad\theta_{0}}} \right)} + {U_{1}\left( {{\cos\quad\theta_{0}} - {\mathbb{i}sin\theta}_{0}} \right)}}} \\{= {U_{0} + {2U_{1}\cos\quad\theta_{0}}}}\end{matrix}$

That is, the phase of the complex amplitude distribution U can be set assubstantially zero by using the three values. Therefore, the secondaryderivative of the complex amplitude distribution U can be of course setas substantially zero as well. It is to be noted that a combination of0, +θ₀ and −θ₀ is used in this example, but there are other combinationsby which a calculation result of Expression (1) becomes a phase zero(substantially zero). Besides the ternary modulation method, it ispossible to use a modulation method utilizing a plurality of values,e.g., four values or five values. Moreover, as to the light modulationelement, the description has been given as to the example where thephase value of the complex amplitude distribution is substantially zeroin the image space of the image formation optical system 3, the phasevalue does not have to be substantially zero as long as the secondaryderivative can be set as substantially zero.

A light intensity I obtained by using the ternary modulation method canbe approximately represented by the following Expression (4).I≈{2D cos θ+(1−2D)}²  (4)

In Expression (4), θ is an absolute value of two modulation phase valueshaving different signs and the same absolute value. D is an occupiedarea ratio of two phase-modulation areas which vary in accordance withthe same pattern. The occupied area ratio D of each phase-modulationarea with respect to the reference phase area takes a value between 0and 0.5.

The fact “the light modulation element has such a complex amplitudetransmittance distribution that the secondary derivative of the phasevalue of the complex amplitude distribution is nearly zero orsubstantially zero at the minimum light intensity portion (the bottomportion of an inverse peak pattern) of the V-shaped light intensitydistribution in the image space of the image formation optical system”means nothing else that the following Expression (5) and (6) aresatisfied taking Expression (1) into consideration. In Expression (5)and (6), (X,Y) is an in-plane coordinate of the light modulationelement, T(X,Y) is a complex amplitude transmittance distribution of thelight modulation element, (x,y) is an in-plane coordinate of the imagesurface of the image formation optical system, ∫ is an integrationsymbol in the point spread function range of the image formation opticalsystem where a point on the light modulation element corresponding tothe point (x,y) on the image surface is the center, and arg is afunction which is used to obtain a phase value.(δ²/δx²)arg(∫T(X,Y)dXdY)≈0  (5)(δ²/δy²)arg(∫T(X,Y)dXdY)≈0  (6)

A description will now be given as to a principle of the defocus methodas the second technique with reference to FIGS. 8A and 8B of convolutionassociated with FIGS. 6A and 6B.

In the defocus method, a predetermined defocus position is intentionallyassumed as a pseudo-focus position, and an irradiation target surface isset at the assumed pseudo-focus position. In this example, as thepseudo-focus position, there is used a position at which a changequantity of a phase of the complex amplitude distribution U involved bydefocusing is relatively small. In FIGS. 8A and 8B, a new defocusposition having a defocus quantity of d0 (d=d0) is assumed as thepseudo-focus position.

In this case, the pseudo-symmetry which is not the perfect symmetry withrespect to a phase value of U×Z can be obtained with the second defocusposition (d=d0) as the pseudo-focus position being determined at thecenter. Since a light intensity distribution at this new lightirradiation position, i.e., the pseudo-focus position is different froma light intensity distribution at the true focus position (a focalposition) to some extent, it is desirable to correct a pattern of thelight modulation element in order to compensate a quantity of differencebetween the light intensity distributions. As a technique for thiscorrection, although not restricted to a certain type, there is a methodwhich corrects an occupied area ratio of the phase-modulation area withrespect to the reference phase area, for example.

FIG. 9 is a view schematically showing a phase pattern of a ternarymodulation type light modulation element according to this embodiment.The light modulation element 1 according to this embodiment is a ternarymodulation type light modulation element based on the first techniquementioned above, and has a reference phase area (indicated by a blankportion in the figure) 1 a having a reference phase value of 0 degree,each rectangular first phase-modulation area (indicated by a shadedportion in the figure) 1 b having a modulation phase value of 60degrees, and each rectangular second phase-modulation area (indicated bya black portion in the figure) 1 c having a modulation phase value of−60 degrees. In this example, the phase-modulation areas 1 b and 1 c arearranged in a matrix form in vertical and horizontal directions (alateral direction (X cross section) and a direction orthogonal to theformer direction) in accordance with a pitch of 5 μm.

An occupied area ratio (a duty) of the first phase-modulation area 1 band an occupied area ratio of the second phase-modulation area 1 clinearly vary between 0% and 25% along the horizontal direction in thedrawing (along the X cross section). Specifically, an occupied arearatio of the first phase-modulation area 1 b is 0% on both sides of thephase pattern along the horizontal direction, and an occupied area ratioof the first phase-modulation area 1 b is 25% at the center. Likewise,an occupied area ratio of the second phase-modulation area 1 c is 0% onboth sides of the phase pattern along the horizontal direction, and anoccupied area ratio of the first phase-modulation area 1 c is 25% at thecenter.

Moreover, a group of first phase-modulation areas 1 b and a group ofsecond phase-modulation areas 1 c whose occupied area ratios vary inaccordance with the same pattern along the horizontal direction (alongthe X cross section) in the figure are alternately formed in theperpendicular direction in the drawing. A unit area which includes thephase-modulation areas 1 b and 1 c and is defined by a pitch of 5 μm,i.e., a rectangular unit area of 5 μm×10 μm (a rectangular unit areawhich includes one phase-modulation area 1 b and one phase-modulationarea 1 c and is indicated by a broken line in FIG. 9) has dimensionswhich are not greater than the point spread function range of the imageformation optical system 3. In other words, the ternary modulation typelight modulation element 1 according to this embodiment has a phasemodulation unit whose dimensions (dimensions converted into acounterpart on the light modulation element 1) are not greater than thepoint spread function range of the image formation optical system 3.

As described above, the ternary modulation type light modulation element1 according to this embodiment has three types of phase areas (1 a, 1 band 1 c) having different fixed phase values (0 degree, 60 degrees and−60 degrees), and occupied area ratios of these areas vary in accordancewith a predetermined pattern. The “fixed phase value” means a phasevalue fixedly set over a given area. In this example, the three types ofphase areas (1 a, 1 b and 1 c) are the reference phase area 1 a havingthe reference phase value of 0 degree as a reference, the firstphase-modulation area 1 b having the first modulation phase value (60degrees) which is a phase-modulation having a positive value, and thesecond phase-modulation area 1 c having the second phase-modulation (−60degrees) which is a phase-modulation having a negative value. A patternwith which an occupied area ratio of the first phase-modulation area 1 bwith respect to the reference phase area 1 a varies is equal to apattern with which an occupied area ratio of the second phase-modulationarea 1 c with respect to the reference phase area 1 a varies. Theternary modulation type light modulation element 1 according to thisembodiment is a light modulation element based on the first techniqueaccording to the present invention as mentioned above, and is designedto have such a complex amplitude transmittance distribution that asecondary derivative of a phase value of the complex amplitudedistribution becomes substantially zero at a bottom portion of aV-shaped light intensity distribution in an image space of the imageformation optical system 3.

The pattern shown in FIG. 9 is one of many equal patterns of an actuallight modulation element, and it can be understood that many lightintensity distributions having an inverse peak pattern or a V shape canbe simultaneously formed by arranging the light modulation element sothat these patterns are repeated in a direction of the X cross section,and the minimum light intensity portion has a linear shape by arrangingthe light modulation element so that these patterns are repeated in adirection orthogonal to the direction of the X cross section.

The aforementioned light modulation element is an optical element whichmodifies a phase of an incident light beam to form a V-shaped lightintensity distribution having a bottom portion of a minimum lightintensity on a determined surface. The light irradiation apparatus is adevice in which the light beam modulated by the light modulation elementirradiates the predetermined surface such as an irradiation surface of atarget (for example, a non-crystal surface), by an image formationsystem to form said V-shaped light intensity distribution on saidsurface.

The light modulation element is formed by a transparent substrate suchas quartz glass substrate having a transparency for the incident lightbeam, as shown in FIG. 9. In the upper surface of the substrate thereare formed a plurality of rectangular recess portions (corresponding toregions 1 b) of different areas as first phase-modulation areas orregions having a positive phase value except for 180 degrees. Therectangular recess portions may be formed by a conventionalphotolithography technique such as a dry etching. In the invention, as amark of the modulation phase value, positive mark represents aphase-proceeding state, and negative mark shows a phase delaying state.

More specifically, the recess portions may be formed as follows. Aresist film is formed on an upper surface of the quartz glass substrate,and then the film is selectively exposed using a chrome mask in anexposing step. Next, a developing step is accomplished for the exposedresist film to form a resist pattern on the substrate. The upper surfaceof the substrate is selectively dry-etched using the resist pattern.Then, the resist pattern is removed from the substrate, so that aplurality of recess portions are formed in the upper surface of thesubstrate.

At portions of the transparent substrate proximate to the firstphase-modulation areas or regions, there are also formed a plurality ofsecond phase-modulation areas each having a negative phase value ofother than 180 degrees. The second phase-modulation regions havedifferent areas. The second regions (corresponding to the areas 1 c inFIG. 9) may also shaped in a rectangular projection, and have sameplane-size, plane-shape and pattern as the first regions. The absolutevalue of the phase value of positive and negative marks equals, and maybe any degree other than 180 degrees, for example 60 degrees.

The second phase-modulation regions 1 c may be so formed that afterformation of the first phase-modulation regions 1 b, the same etchingprocess as formation of the first regions is applied to the uppersurface of the substrate, using a pattern corresponding to the secondregions. Alternately the steps forming the first and second regions maybe reverse, that is the first regions 1 b may be formed after the secondregions 1 c are formed.

Next, there will now be described one example of manufacturing theaforementioned light modulation element with reference to FIGS. 9A to9G.

A quartz glass substrate 61 as a transparent substrate for the lightmodulation element is prepared, as shown in FIG. 9A. Next, as shown inFIG. 9B, a resist film 62 is formed on an upper surface of the substrate61. The resist film 62 is selectively exposed with light, using a maskfor forming first or second phase-modulation areas (In this embodiment,first phase-modulation areas). Then, the resultant resist film 62 isselectively etched to form a resist pattern 63 for firstphase-modulation areas on the upper surface of the substrate 61, asshown in FIG. 9C. The upper surface of the substrate 61 is selectivelyetched, using the resist pattern 63, and then the resist pattern 63 isremoved from the substrate, so that first phase-modulation areas 64 areformed on the upper surface of the substrate 61, as shown in FIG. 9D.

Next, second phase-modulation areas are formed on the substrate to bejuxtaposed with the first phase-modulation areas as follows.

First, a resist film is formed on the upper surface of the substrate 61on which the first phase-modulation areas 64 have been provided. Theresist film is selectively exposed with light, using a mask for formingsecond phase-modulation areas. Then, the resultant resist film isselectively etched to form a resist pattern 65 for secondphase-modulation areas on the upper surface of the substrate 61, asshown in FIG. 9E. The portions of the upper surface of the substrate 61,which are not covered with the second pattern 65 are selectively etched,using the resist pattern 65, as shown in FIG. 9F. Next, the resistpattern 65 is removed from the substrate, so that a reference phase area1 a, and first and second phase-modulation areas 1 b and 1 c are formedon the upper surface of the substrate 61, as shown in FIG. 9G. Thedimensions and arrangement of the first and second phase modulationregions 1 b and 1 c of a square shape are set as shown in FIG. 9. Morespecifically, the first and second phase-modulation regions are arrangedin rows (lateral direction) and columns in each unit. The rows are oftwo types, one consisting of first regions 1 b, and the other consistingof second regions 1 c. The rows of two types are alternately arranged.In each row of either type, the middle region the largest, and the otherregions on either sides of the largest gradually decreased in sizetoward the end of the column in the unit. The first and second regions 1b and 1 c forming each column have the same size.

The shape of the regions 1 b and 1 c is not limited to theaforementioned square, and may be a suitable shape having a desiredarea, such as circular, ellipse or triangle.

Next, there will be described an example of forming a phase-modulationregion having a desired phase value on a quartz glass substrate.

The phase value for phase-modulating an incident light beam may beprovided, for example, by forming steps on a light-incident surface ofthe substrate. The phase modulation for the incident light beam occursdue to difference of indexes of refraction on both sides of the boundary(step).

Thickness of the step is represented by the following equation.T=λΦ/2π(n−1)Here, λ is a wave length of the incident light beam, Φ a phase valuerepresented by radian, and n an index of refraction of a materialforming the step. Thus, the desired step t may be obtained by selectinga substrate material having an index of refraction and an incident lighthaving a wavelength. These constants may be set by forming a film on atransparent substrate by a material having a desired index ofrefraction, using such as PECVD or LPCVD, or etching the surface of atransparent substrate.

Although the light modulation element shown in FIG. 9 is formed byarranging the rectangular phase-modulation areas in a matrix form, theshapes and/or arrangements of the phase-modulation areas are notrestricted thereto. For example, the phase-modulation area may have anyother shape such as a circular shape, and any other arrangementconformation such as a zigzag arrangement can be adopted.

FIGS. 10A to 10C are views each showing a V-shaped light intensitydistribution formed through the image formation optical system when theternary modulation type light modulation element according to thisembodiment is used. The light intensity distribution shown in each ofthese drawings is calculated on the assumption that a wavelength λ of alight is 248 nm, an image side numerical aperture NA of the imageformation optical system 3 is 0.13, an image formation magnification ofthe image formation optical system 3 is ⅕ and a value δ (a coherencefactor) of the image formation optical system 3 is 0.47. Additionally,FIG. 10B shows a light intensity distribution obtained at a focusposition along the X cross section, FIG. 10A shows a light intensitydistribution obtained at a defocus position of −5 μm (a positionslightly moved from the focus position by 5 μm in a direction closer tothe image formation optical system 3) along the X cross section, andFIG. 10C shows a light intensity distribution obtained at a defocusposition of +5 μm (a position slightly moved from the focus position by5 μm in a direction apart from the image formation optical system 3)along the X cross section.

When the ternary modulation type light modulation element 1 according tothis embodiment is used, as shown in FIG. 10B, a substantially idealV-shaped light intensity distribution is formed at the focus position(the image formation surface) of the image formation optical system 3.Further, even if the irradiation target surface is defocused by ±5 μm asshown in FIGS. 10A and 10C, a shape of the V-shaped light intensitydistribution formed on the irradiation target surface slightly changesdue to defocusing, and this change is substantially symmetrical(symmetrical in the lateral direction with the minimum light intensityportion being determined at the center) without being dependent on adirection of defocusing. In this embodiment, in order for production ofthe light modulation element 1 to become relatively each, occupied arearatios of the phase-modulation areas 1 b and 1 c are set to 0 to 0.25,and the V-shaped light intensity distribution with a relatively shallowbottom is realized.

As described above, the crystallization apparatus according to thisembodiment uses a light modulation element, e.g., a ternary modulationtype light modulation element 1 having such a complex amplitudetransmittance distribution that a secondary derivative of a phase valueof a complex amplitude distribution becomes substantially zero at abottom portion of a V-shaped light intensity distribution in an imagespace of the image formation optical system 3. Therefore, a desiredV-shaped light intensity distribution can be stably formed without beingsubstantially affected by defocusing caused due to a board thicknessdeviation unavoidably existing in, e.g., the processed substrate 4,thereby substantially evenly generating crystal grains on asemiconductor film. Further, in this embodiment, since a substantiallyideal V-shaped light intensity distribution may be stably formed,crystal grains can be formed in a semiconductor film with a high fillingfactor.

It is to be noted that the ternary modulation type light modulationelement 1 based on the first technique according to the presentinvention is used in the foregoing embodiment, it is also possible touse a modification in which the defocus method as the second techniqueaccording to the present invention is applied while utilizing the binarymodulation type light modulation element 10 shown in FIG. 14. FIGS. 11Ato 11C and FIGS. 12A and 12B are views each schematically showing aV-shaped light intensity distribution formed through the image formationoptical system when the binary modulation type light modulation element10 is used. In this example, FIG. 11A corresponds to a defocus positionof −5 μm; FIG. 11B, a focus position; FIG. 11C, a defocus position of +5μm; FIG. 12A, a defocus position of +10 μm; and FIG. 12B, a defocusposition of +15 μm.

Referring to FIGS. 12A and 12B, it can be understood that a shape of theV-shaped light intensity distribution hardly changes between the defocusposition of +10 μm and the defocus position of +15 μm. Therefore, in themodification of this embodiment, the binary modulation type lightmodulation element 10 shown in FIG. 14 is used, a defocus position of,e.g., +12.5 μm is assumed as a pseudo-focus position, and an irradiationtarget surface of the processed substrate 4 is set at this pseudo-focusposition. As a result, even in the modification, a desired V-shapedlight intensity distribution can be stably formed without beingsubstantially affected by defocusing caused due to, e.g., a boardthickness deviation unavoidably existing in the processed substrate 4,and hence crystal grains can be substantially evenly generated on asemiconductor film.

In the defocusing process, it is possible to obtain ideal lightintensity distributions at defocusing positions, as shown in FIG. 12C,by correcting an occupied area ration of the conventional phase shifteras shown in FIG. 14. In the exampled modified phase shifter, dimensionsof the modulation-phase areas at the center of each unit of the phaseshifter shown in FIG. 14 are changed to correct the occupied area ratiosat the center. For example, in the conventional phase shifter, actualdimensions (conversion value on the projected plane of length of oneside of the square modulation-phase area) of the largest and secondlargest modulation-phase areas are 0.354 μm and 0.335 μm to set theoccupied area ratios to 50% and 40%, respectively, while in thecorrected phase shifter, actual dimensions of the largest and secondlargest modulation-phase areas are 0.296 μm and 0.278 μm to set theoccupied area ratios to 35% and 31%, respectively. This correction isonly one example, and the occupied area ratio may be varied at thedesired position of the phase shift to various values.

FIGS. 13A to 13E are process cross-sectional views showing processes formanufacturing an electronic device in an area crystallized by using thecrystallization apparatus according to this embodiment. As shown in FIG.13A, there is prepared a processed substrate 5 obtained by forming anunderlying film 81 (e.g., a laminated film of SiN with a film thicknessof 50 nm and SiO₂ with a film thickness of 100 nm) and an amorphoussemiconductor film 82 (e.g., Si, Ge, SiGe or the like having a filmthickness of approximately 50 nm to 200 nm) on an insulating substrate80 (e.g., alkali glass, quartz glass, plastic, polyimide or the like) bya chemical vapor deposition method or a sputtering method. Further, apredetermined area on a surface of the amorphous silicon film 82 isirradiated with a laser light 83 (e.g., a KrF excimer laser light or anXeCl excimer laser light) by using the crystallization apparatusaccording to this embodiment.

In this manner, as shown in FIG. 13B, a polycrystal semiconductor filmor a single-crystallized semiconductor film 84 having a crystal with alarge particle size is generated. Then, as shown in FIG. 13C, thepolycrystal semiconductor film or the single-crystallized semiconductorfilm 84 is processed into an island-shaped semiconductor film 85 whichbecomes an area in which, e.g., a thin film transistor is formed byusing a photolithography technique, and an SiO₂ film with a filmthickness of 20 nm to 100 nm is formed as a gate insulating film 86 on asurface of the semiconductor film 85 by using the chemical vapordeposition method or the sputtering method. Furthermore, as shown inFIG. 13D, a gate electrode 87 (e.g., silicide or MoW) is formed on thegate insulating film, and impurity ions 88 (phosphor in case of an Nchannel transistor, and boron in case of a P channel transistor) areimplanted with the gate electrode 87 being used as a mask. Thereafter,annealing processing (e.g., one hour at 450° C.) is performed in anitrogen atmosphere, and impurities are activated so that a source area91 and a drain area 92 are formed to the island-shaped semiconductorfilm 85. Subsequently, as shown in FIG. 13E, an interlayer insulatingfilm 89 is formed and contact holes are formed in order to form a sourceelectrode 93 and a drain electrode 94 which are connected with a source91 and a drain 92 through a channel 90.

In the above-described processes, the channel 90 is formed in accordancewith a position of a crystal with a large particle size of thepolycrystal semiconductor film or the single-crystallized semiconductorfilm 84 generated in the processes shown in FIGS. 13A and 13B. With theabove-described processes, a polycrystal transistor can be formed or athin film transistor (TFT) can be formed to the single-crystallizedsemiconductor. The thus manufactured polycrystal transistor orsingle-crystallized transistor can be applied to a drive circuit for aliquid crystal display unit (a display) or an EL (electroluminescence)display or an integrated circuit such as a memory (an SRAM or a DRAM) ora CPU.

It is to be noted that the present invention is applied to thecrystallization apparatus and the crystallization method which generatea crystallized semiconductor film by irradiating a polycrystalsemiconductor film or an amorphous semiconductor film with a lighthaving a predetermined light intensity distribution. However, thepresent invention is not restricted thereto, and it can be generallyapplied to a light irradiation apparatus which forms a predeterminedlight intensity distribution on a predetermined surface through theimage formation optical system.

Additional advantages and modifications will readily occur to thoseskilled in the art. Therefore, the invention in its broader aspects isnot limited to the specific details and representative embodiments shownand described herein. Accordingly, various modifications may be madewithout departing from the spirit or scope of the general inventionconcept as defined by the appended claims and their equivalents.

1. A light irradiation apparatus comprising: a light modulation elementwhich modulates a phase of an incident light beam to obtain a V-shapedlight intensity distribution having a bottom portion of a minimum lightintensity; and an image formation optical system which applies themodulated light beam from the light modulation element to an irradiationtarget surface in such a manner that the V-shaped light intensitydistribution is provided on the irradiation target surface, wherein thelight modulation element has such a complex amplitude transmittancedistribution that a secondary derivative of a phase value of a complexamplitude distribution becomes substantially zero at the bottom portionof the V-shaped light intensity distribution in an image space of theimage formation optical system.
 2. The light irradiation apparatusaccording to claim 1, wherein the following conditions are satisfied:(δ²/δx²)arg(∫T(X,Y) dXdY)≈0(Δ²/δy²)arg(∫T(X,Y)dXdY)≈0 wherein (X,Y) is an in-plane coordinate ofthe light modulation element, T(X,Y) is a complex amplitudetransmittance distribution of the light modulation element, (x,y) is anin-plane coordinate of an image surface of the image formation opticalsystem, ∫ is an integration symbol in a point spread function range ofthe image formation optical system where a point on the light modulationelement corresponding to a point (x,y) on the image surface is thecenter, and arg is a function which is used to obtain a phase value. 3.The light irradiation apparatus according to claim 1, wherein thecomplex amplitude transmittance distribution of the light modulationelement has a phase modulation unit whose dimension is not greater thanthe point spread function range of the image formation optical system.4. The light irradiation apparatus according to claim 1, wherein thelight modulation element has at least three types of phase areas havingfixed phase values different from each other, and occupied area ratiosof the phase areas vary in accordance with a predetermined pattern. 5.The light irradiation apparatus according to claim 1, wherein the lightmodulation element comprises, as at least three types of phase areas, areference phase area having a reference phase value of 0 degree as areference, a first phase-modulation area having a first modulation phasevalue which is a phase-modulation having a positive value, and a secondphase-modulation area having a second modulation phase value which is aphase-modulation having a negative value whose absolute value issubstantially equal to that of the first modulation phase value.
 6. Thelight irradiation apparatus according to claim 5, wherein a pattern withwhich an occupied area ratio of the first phase-modulation area withrespect to the reference phase area varies is substantially equal to apattern with which an occupied area ratio of the second phase-modulationarea with respect to the reference phase area varies.
 7. A lightirradiation method having a light modulation element which modulates anincident light beam, and an image formation optical system which appliesa light beam with a V-shaped light intensity distribution having abottom portion of a minimum light intensity to an irradiation targetsurface, wherein the irradiation target surface is positioned at such aposition that a secondary derivative of a phase value of a complexamplitude distribution becomes substantially zero at the bottom portionof the V-shaped light intensity distribution in an image space of theimage formation optical system, and the irradiation target surface isirradiated with a light.
 8. A crystallization apparatus comprising: thelight irradiation apparatus defined in claim 1; and a stage which holdsa processed substrate including a non-single-crystal semiconductor filmhaving the irradiation target surface on an image formation surface ofthe image formation optical system.
 9. A crystallization method whichapplies a light having the V-shaped light intensity distribution to theprocessed substrate having a non-single-crystal semiconductor film setas the irradiation target surface to generate a crystallizedsemiconductor film by using the light irradiation apparatus defined inclaim
 1. 10. A device manufactured by using the crystallization methoddefined in claim
 9. 11. A light modulation element which modulates aphase of an incident light beam so that a V-shaped light intensitydistribution is provided on an irradiation target surface, comprising:at least three types of phase areas having fixed phase values differentfrom each other, occupied area ratios of the phase areas varying inaccordance with a predetermined pattern.
 12. The light modulationelement according to claim 11, comprising, as at least three types ofphase areas, a reference phase area having a reference phase value of 0degree as a reference, a first phase-modulation area having a firstmodulation phase value which is a phase-modulation having a positivevalue, and a second phase-modulation area having a second modulationphase value which is a phase-modulation having a negative value whoseabsolute value is substantially equal to that of the first modulationphase value.
 13. The light modulation element according to claim 12,wherein a pattern with which an occupied area ratio of the firstphase-modulation area with respect to the reference phase area varies issubstantially equal to a pattern with which an occupied area ratio ofthe second phase-modulation area with respect to the reference phasearea varies.
 14. A light irradiation apparatus comprising: a lightmodulation element which modulates a phase of an incident light beam toobtain a V-shaped light intensity distribution having a bottom portionof a minimum light intensity; and an image formation optical systemwhich applies the modulated light beam from the light modulation elementto an irradiation target surface in such a manner that the V-shapedlight intensity distribution is provided on the irradiation targetsurface, the light modulation element including: a transparent substratewhich has at least one surface for passing the incident light beam; areference phase region provided on the surface of the substrate; firstphase-modulation regions having a positive modulation value for thereference phase region, except for 180 degrees; and secondphase-modulation regions having a negative modulation value for thereference phase region, except for 180 degrees, wherein absolute valuesof the positive and negative modulation phase values are identical, andthe first and second phase-modulation regions have the same shape, andare arranged to be juxtaposed with each other so that their areas changeone by one in a lateral direction.
 15. The A light irradiation apparatusaccording to claim 14, wherein said first phase-modulation regionsinclude rectangular recess regions formed on the surface of thetransparent substrate and arranged in a pattern in which the recessregions are juxtaposed with each other so that their areas change one byone in the lateral direction, and said second phase-modulation regionsrectangular projected regions formed on the surface of the transparentsubstrate to juxtapose with the recess regions and arranged in the samepattern as the recess regions.
 16. A light modulation element formodulating an incident light beam so that the modulated light beam has aV-shaped light intensity distribution on an irradiation target surface,comprising: a transparent substrate which has at least one surface forpassing the incident light beam; a reference phase region provided onthe surface of the substrate; first phase-modulation regions having apositive modulation value for the reference phase region, except for 180degrees; and second phase-modulation regions having a negativemodulation value for the reference phase region, except for 180 degrees,wherein absolute values of the positive and negative modulation phasevalues are identical, and the first and second phase-modulation regionshave the same shape, and are arranged to be juxtaposed with each otherso that their areas change one by one in a lateral direction.
 17. Thelight modulation element according to claim 16, wherein said firstphase-modulation regions include rectangular recess regions formed onthe surface of the transparent substrate and arranged in a pattern inwhich the recess regions are juxtaposed with each other so that theirareas change one by one in the lateral direction, and said secondphase-modulation regions rectangular projected regions formed on thesurface of the transparent substrate to juxtapose with the recessregions and arranged in the same pattern as the recess regions.